Stored Energy in a pressure vessel

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SUMMARY

The discussion focuses on modeling the energy dynamics of a pressure vessel containing compressed natural gas at approximately 250 times atmospheric pressure. The user seeks to approximate the energy lost during gas release using the kinetic energy formula (1/2 mv^2) and questions whether this can be equated to the change in stored energy in the tank, modeled as E = PV. The user acknowledges the assumption of an isochoric process, leading to confusion regarding the relationship between stored energy and work done during gas release.

PREREQUISITES
  • Understanding of thermodynamics, specifically gas laws
  • Familiarity with kinetic energy calculations
  • Knowledge of isochoric and isobaric processes
  • Basic principles of pressure and volume relationships in gas systems
NEXT STEPS
  • Research the implications of isochoric versus isobaric processes in thermodynamics
  • Explore the derivation and applications of the ideal gas law (PV=nRT)
  • Learn about energy conservation principles in fluid dynamics
  • Investigate methods for modeling transient gas flow in pressure vessels
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Engineers, physicists, and students studying thermodynamics or fluid mechanics, particularly those interested in energy storage and release in compressed gas systems.

boka33
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Consider a problem where a tank holds compressed natural gas, compressed to approx. 250 times atmospheric conditions.

Now release the tank valve letting some of the gas out.

Assuming a small timestep, I can approximate the energy lost as 1/2 mv^2,

where m is the mass released during the timestep, and v is the (assumed constant for small timestep) velocity of exiting gas.

Can I equate this to the change in stored energy in the tank during this timestep with reasonable accuracy?

If so, can I model the stored energy as E = PV

where P is pressure in the tank and V is the volume.

Thanks a lot.
 
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I think the difference is that I was assuming an isochoric process, since a tank of fixed volume held the process. Maybe this is not the case? Either way, it should be noted that in my case I am just looking for a valid approximation, so I do not wish to model a differential problem. I have been using timesteps.

So if isochoric is assumed

Work = PdV = 0

But I am looking at stored energy, not work done, this is where I am confused.
 
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